Assume the animal’s brain more or less resembles that of an average sized mammal (similar in size and properties of the brain of homo sapiens sapiens).

This is a fallacious assumption, Homo sapiens have very large cerebral hemispheres, "lower" mammals do not, birds none at all. A hit to the cerebral hemispheres alone will not kill a human, there are many, many documented cases of people shot in the head who survived. The goal is not to hit "the brain" per se, the goal is to hit a vital part of the brain, i.e. the brain stem. The brain stem (medulla oblongata, pons, midbrain) controls autonomic functions, equilibrium, coordination, and basic sensory functions. So, you need to impact the brainstem. Having witnessed the killing of millions (literally) of animals, the way you do that is to draw an X from each ear to the opposite eye, and shoot where the lines cross. The animal will collapse on the spot.

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You aim for the brain point blank, but what angle/impact point do you pick and what kind of round do you use:

Killing an animal does not take much energy, any of the choices you listed would be sufficient if you hit the right spot. I have seen 2,000 lbs bulls dropped where they stood with a single shot to the forehead from a 22. I have seen rabbits shot with shotguns that run off never to be found. Placement counts.